Answer to Question #105763 in Geometry for John Lloyd

Question

Given triangle ABC whose sides AB=15 in, AC=25, BC=30. From point D on side AB, a line DE is drawn to point AC such that angle ADE is equal to angle ABC. If perimeter of ADE is 28 in, find the length of segments BD and CE

Answer 1

since DE and BC are parallel, triangles ABC and ADE are similar.

The ratio of sides of ADE to ABC = 28/70 = 2/5

So,

CE = AC * 3/5 = 15

BD = AB * 3/5 = 9